As someone both studying and teaching math: there should be two different ways to teach math - for other mathematicians and for non-mathematicians.
For mathematicians you want to use all the formal proofs and sharp definitions and so on. But we have so much fun teaching that way, we forget when we switch classes that engineers don’t like/care/are motivated to think the same way. We should pivot towards application-based, result-oriented teaching but we often just don’t. And students have to deal with it because the other class managed (pure mathematicians).
Yes this. Most math instructors teach like we’re math majors and are in it for the dirty abstract and “obvious” details that they forget most of us will never use it when working on machines or even some basic programming. Their insistence on teaching in their often inefficient way acts as a filter for so many otherwise promising engineers.
It’s not about not teaching the platonic definition.
The problem is that you don’t start at the platonic definition. Mathematicians don’t start there either, they start at a problem. The problem may even be a hole in some other platonic idea, but nothing is ever self-contained Platonism… except maybe for categories, but well, the problem it looks is how far pure Platonism can get you.
Yes, people teach mathematics wrong. It should start from application, and only then get formalized.
A large part of the problem is that we put people that study pure math deciding how to teach it.
As someone both studying and teaching math: there should be two different ways to teach math - for other mathematicians and for non-mathematicians.
For mathematicians you want to use all the formal proofs and sharp definitions and so on. But we have so much fun teaching that way, we forget when we switch classes that engineers don’t like/care/are motivated to think the same way. We should pivot towards application-based, result-oriented teaching but we often just don’t. And students have to deal with it because the other class managed (pure mathematicians).
Yes this. Most math instructors teach like we’re math majors and are in it for the dirty abstract and “obvious” details that they forget most of us will never use it when working on machines or even some basic programming. Their insistence on teaching in their often inefficient way acts as a filter for so many otherwise promising engineers.
Yes, that’s exactly why many universities have classes like ‘maths for electrical engineering’
It’s not about not teaching the platonic definition.
The problem is that you don’t start at the platonic definition. Mathematicians don’t start there either, they start at a problem. The problem may even be a hole in some other platonic idea, but nothing is ever self-contained Platonism… except maybe for categories, but well, the problem it looks is how far pure Platonism can get you.